Geometric presentations of Lie groups and their Dehn functions
Group Theory
2017-07-11 v2 Geometric Topology
Rings and Algebras
Abstract
We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels' theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.
Keywords
Cite
@article{arxiv.1310.5373,
title = {Geometric presentations of Lie groups and their Dehn functions},
author = {Yves Cornulier and Romain Tessera},
journal= {arXiv preprint arXiv:1310.5373},
year = {2017}
}
Comments
137 pages, a few figures. v1->v2: the paper has been thoroughly reorganized in order to be more readable. The numbering of theorems is therefore modified